Lecture Notes for Laplace Transform

← Back to document page

Lecture Notes for Laplace TransformWen ShenApril 2009NB! These Notes are used by myself. They are provided to students as a supplement to thetextbook. They can not substitute the textbook. Laplace Transform is used to handle piecewise continuous or impulsive : Definition of the Laplace Transform (1)Topics: Definition of Laplace Transform , Compute Laplace Transform by definition, including piecewise continuous :Given a functionf(t),t 0, its Laplace transformF(s) =L{f(t)}is defined asF(s) =L{f(t)}.= 0e stf(t) limA A0e stf(t)dtWe say the Transform converges if the limit exists, and diverges if we will give examples on computing the Laplace Transform of given functions by (t) = 1 fort (s) =L{f(t)}= limA A0e st 1dt= limA 1se st A0= limA 1s[e]

Solutions of initial value problems. We will go through one example flrst. Example 14. (Two distinct real roots.) Solve the initial value problem by Laplace transform,

  Solutions, Transform, Laplace transforms, Laplace